Statistics for dark matter subhalo searches in gamma rays from a kinematically constrained population model: Fermi-LAT-like telescopes

Cold dark matter subhalos are expected to populate galaxies in numbers. If dark matter self-annihilates, these objects turn into prime targets for indirect searches, in particular with gamma-ray telescopes. Incidentally, the Fermi-LAT catalog already contains many unidentified sources that might be associated with subhalos. In this paper, we determine the probability for subhalos to be identified as gamma-ray pointlike sources from their predicted distribution properties. We use a semi-analytical model for the Galactic subhalo population, which, in contrast to cosmological simulations, can be made fully consistent with current kinematic constraints in the Milky Way and has no resolution limit. The model incorporates tidal stripping effects from a realistic distribution of baryons in the Milky Way. The same baryonic distribution contributes a diffuse gamma-ray foreground which adds up to that, often neglected in subhalo searches, generated by the smooth dark matter and the unresolved subhalos. This configuration implies a correlation between pointlike subhalo signals and diffuse background. Based on this semi-analytical modeling, we generate mock gamma-ray data assuming an idealized telescope resembling Fermi-LAT and perform a likelihood analysis to estimate the current and future sensitivity to subhalos in the relevant parameter space. We find a number of detectable subhalos of order ${\cal O}(<1)$ for optimistic model parameters and a WIMP mass of 100~GeV, maximized for a cored host halo. This barely provides support to the current interpretation of several Fermi unidentified sources as subhalos. We also find it more likely to detect the smooth Galactic halo itself before subhalos, should dark matter in the GeV-TeV mass range self-annihilate through $s$-wave processes.